The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 4 (2015) no. 3, pp. 95-108
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In this paper we consider the approach to search for systems of orthogonal Latin Squares, that is based on reducing the corresponding problems to Boolean Satisfiability problem. We constructed the SAT encoding for finding orthogonal diagonal Latin Squares of order 10. Using this encoding and the resources provided by the volunteer computing project SAT@home we managed to find 17 previously unknown pairs. Based on these 17 pairs and on 3 previously published pairs we constructed the pseudotriples of diagonal Latin Squares of order 10. To construct pseudotriples we employed the computing cluster. The last step required us to make parallel implementation of the algorithm for generating diagonal Latin Squares of order 10.
Keywords:
Latin squares, volunteer computing, Boolean satisfiability problem, SAT@home project.
@article{VYURV_2015_4_3_a7,
author = {O. S. Zaikin and S. E. Kochemazov},
title = {The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project {SAT@home}},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
pages = {95--108},
publisher = {mathdoc},
volume = {4},
number = {3},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURV_2015_4_3_a7/}
}
TY - JOUR AU - O. S. Zaikin AU - S. E. Kochemazov TI - The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika PY - 2015 SP - 95 EP - 108 VL - 4 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURV_2015_4_3_a7/ LA - ru ID - VYURV_2015_4_3_a7 ER -
%0 Journal Article %A O. S. Zaikin %A S. E. Kochemazov %T The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika %D 2015 %P 95-108 %V 4 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURV_2015_4_3_a7/ %G ru %F VYURV_2015_4_3_a7
O. S. Zaikin; S. E. Kochemazov. The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 4 (2015) no. 3, pp. 95-108. http://geodesic.mathdoc.fr/item/VYURV_2015_4_3_a7/